Flares and their echoes can help distinguish photon rings from black holes with space-Earth very long baseline interferometry

Photon rings near the edge of a black hole shadow is supposed to be a unique tool to validate general relativity and provide reliable measurements of principal black hole parameters: spin and mass. Such measurements are possible though only for nearby supermassive black holes (SMBH) with Space-Earth Very Long Baseline Interferometry (S-VLBI) in the submillimeter wavelength range. For subrings to be distinguished S-EVLBI observations with long baselines at the Lagrangian Sun-Earth L2 libration point are needed. However, the average fluxes of nearby SMBH: Sagittarius A$^\ast$ (Sgr A$^\ast$) and M87$^\ast$ -- $F_\nu\sim 1$ Jy, are still insufficient to detect the signal from the photon rings with even such long baselines. We argue that only manifestations of flares in the submillimeter waveband in their accretion disks can reveal observable signals from the photon rings with the S-EVLBI at L2. Such observations will become possible within the planned join program of the {\it Event Horizon Telescope} (EHT) and {\it Millimetron Space Observatory} (MSO), and within the planned {\it next generation EHT} (ngEHT) project. Two different observational tests for photons rings are discussed. The first one involves observations of a time series of responds from subsequent subrings as can be seen in a 1D visibility function within the join EHT-MSO configuration, the second one -- measurements of an increase of the angle between subsequent subrings in the 2D VLBI image which can be obtained within the ngEHT project.